Whether turbulent or laminar flow exists in a tube under given conditions may be predicted on the basis of a dimensionless number called Reynold’s number (NR). This number represents the ratio of inertial to viscous forces. For a fluid flowing through a cylindrical tube,
Equation 17.12 where ρ= fluid density, D = tube diameter, v = mean velocity, and η= viscosity. When NR is 2000 or less, the flow is usually laminar; when NR is 3000 or greater, the flow is turbulent; and when NR is between 2000 and 3000, the flow is transitional between laminar and turbulent.
Eq. 17.12 indicates that high fluid densities, small tube diameters, high flow velocities, and low fluid viscosities predispose to turbulence. In addition to these factors, abrupt variations in tube dimensions or irregularities in the tube walls may produce turbulence.
Shear Stress on the Vessel Wall
As blood flows through a vessel, it exerts a force on the vessel wall parallel to the wall. This force is called a shear stress (τ). Shear stress is directly proportional to the flow rate and viscosity of the fluid:
Equation 17.13
Turbulenceisusuallyaccompaniedbyaudiblevibrations.Turbulentflowwithinthecardiovascularsystemmaybedetectedthroughastethoscopeduringphysicalexamination.Whentheturbulenceoccursintheheart,theresultantsoundistermedamurmur; whenitoccursinavessel,thesoundistermedabruit. Insevereanemia,functionalcardiacmurmurs(murmursnotcausedbystructuralabnormalities)arefrequentlydetectable.Thephysicalbasesforsuchmurmursresidesare(1)thereducedviscosityofbloodinanemiaand (2)thehighflowvelocitiesassociatedwiththehighcardiacoutputthatusuallyprevailsinanemicpatients.Bloodclots,orthrombi,aremorelikelytodevelopinturbulentflowthaninlaminarflow.Aproblemwiththeuseofartificialvalvesinthesurgicaltreatmentofvalvularheartdiseaseisthatthrombimayoccurinassociationwiththeprostheticvalve.Thethrombimaybedislodgedandoccludeacrucialbloodvessel.Itisimportanttodesignsuchvalvestoavertturbulenceandtoincludeanticoagulantsasapartoftherapy.